Related papers: The Depth Poset under Transpositions in the Filter

First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made---for the continuous-time case---in Mallat, 2012, and Wiatowski and B\"olcskei, 2015. This paper considers the discrete case,…

Correlations are known to play a crucial role in determining the structure of complex networks. Here we study how their presence affects the computation of the percolation threshold in random hypergraphs. In order to mimic the correlation…

While convolutional neural networks have shown a tremendous impact on various computer vision tasks, they generally demonstrate limitations in explicitly modeling long-range dependencies due to the intrinsic locality of the convolution…

We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex. Our approach differs from the commonly used reduction algorithm by first computing persistence pairs within local chunks, then…

We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.

Given a functor from any category into the category of topological spaces, one obtains a linear representation of the category by post-composing the given functor with a homology functor with field coefficients. This construction is…

Lattices and periodic point sets are well known objects from discrete geometry. They are also used in crystallography as one of the models of atomic structure of periodic crystals. In this paper we study the embedding properties of spaces…

We create a framework for studying symmetric chain decompositions of families of finite posets based on the geometry of polytopes. Our framework unifies almost all known results regarding symmetric chain decompositions of the Young posets…

Depth estimation attracts widespread attention in the computer vision community. However, it is still quite difficult to recover an accurate depth map using only one RGB image. We observe a phenomenon that existing methods tend to fail in…

We introduce Orthogonal M\"obius Inversion $\mathsf{OI}$, a concept analogous to M\"obius inversion on finite posets, which is applicable to order-preservings functions from a finite poset to the Grassmannian $\mathsf{Gr}(V)$ of an inner…

We propose the Waterfall Transformer architecture for Pose estimation (WTPose), a single-pass, end-to-end trainable framework designed for multi-person pose estimation. Our framework leverages a transformer-based waterfall module that…

Matrix reduction is the standard procedure for computing the persistent homology of a filtered simplicial complex with $m$ simplices. Its output is a particular decomposition of the total boundary matrix, from which the persistence diagrams…

In this paper, we study the persistent homology of the offset filtration of algebraic varieties. We prove the algebraicity of two quantities central to the computation of persistent homology. Moreover, we connect persistent homology and…

The Interval poset of a permutation is an effective way of capturing all the intervals of the permutation and the inclusions between them and was introduced recently by Tenner. Thi paper explores the geometric interpretation of interval…

Depth information which specifies the distance between objects and current position of the robot is essential for many robot tasks such as navigation. Recently, researchers have proposed depth completion frameworks to provide dense depth…

We propose a method to estimate the uncertainty of the outcome of an image classifier on a given input datum. Deep neural networks commonly used for image classification are deterministic maps from an input image to an output class. As…

In this paper we outline several points of view on the interplay between discrete and continuous wavelet transforms; stressing both pure and applied aspects of both. We outline some new links between the two transform technologies based on…

We present a matrix-theoretic approach for studying and enumerating finite posets through their incidence representations, referred to as poset matrices. Naturally labelled posets are encoded as Boolean lower triangular matrices, allowing a…

Solving 6D pose estimation is non-trivial to cope with intrinsic appearance and shape variation and severe inter-object occlusion, and is made more challenging in light of extrinsic large illumination changes and low quality of the acquired…

Multiparameter persistent homology has emerged as a powerful generalization of topological data analysis, capable of encoding multivariate filtrations. However, the algebraic complexity of multiparameter persistence modules, marked by wild…